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An iterative Riemann solver for relativistic hydrodynamics. (English) Zbl 0892.35008
The main motivation of the paper is to find a robust and efficient Godunov scheme for relativistic hydrodynamical flows with strong discontinuity. The authors present an approximate Riemann solver based on jump conditions for shocks which iteratively solves any Riemann problem in relativistic hydrodynamics. The Riemann solver is presented after introducing the basic equations. A few test problems through which the correctness and convergence of the solver are shown. Finally, it is pointed out that the solver is based on the jump conditions for the shocks, and therefore the jump conditions are approximately used for refraction waves, which limits the solver itself to weak refraction waves.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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